One of the best money making opportunities for every player in single deck blackjack is when you get the opportunity to split your pairs. When you are dealt with two cards of the same value (let's say a couple of Eight's or a pair of Tens) you have the option to make your single hand into two hands by adding a new card to each card in your current hand. You also add an equal bet to the new hand you make thus giving you a chance to double your profit.
First item every player should look out for is the dealer's up card that is shown to all players on the blackjack table. Some up cards you can split on and there are others where you simply can't (i.e. if you do split on such cards, thus making a bad move, you could end up losing twice as much as your initial wager).
Next thing you should look out for is the cards in your own hand. Some hands you just have to split, some hands you don't. So make it a habit to check out what card the dealer has and what cards you have and then make your decision.
Here are the right moves when splitting pairs in single deck blackjack:
Pair of Aces: Your only move should be to split this pair of cards. It doesn't matter what card the dealer has.
Pair of Tens: The only correct move is to stand with this pair regardless of what the dealer shows as an up card.
Pair of Nines: Split this pair of cards versus the dealer's two to six, eight, and nine. Stand if the dealer displays a seven, a ten, or an ace.
Pair of Eights: Always split this pair of cards, no other better blackjack alternative.
Pair of Sevens: Split this pair of cards if the dealer has two to seven; hit for an eight, nine, or ace; and stand if the dealer shows a ten.
Pair of Sixes: Split this pair if the dealer shows two to six, everything else you hit.
Pair of Fives: Double down for the dealer's two to nine and hit for a ten or ace.
Pair of Fours: Your only option is to hit until you get a good blackjack hand.
Pair of Threes: Hit if the dealer has a two or three, eight to ten, and ace displayed. Split from four to seven.
Pair of Twos: For every two, eight to ten, and ace the dealer has you need to hit while you split on everything else.
These are your correct moves when playing the pairs in single deck blackjack. Just remember that you don't have to split every single pair in this mode of play.